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Clustering Small Samples with Quality Guarantees: Adaptivity with One2all pps
At the core of our design is the {\em one2all} construction of multi-objective probability-proportional-to-size (pps) samples: Given a set $M$ of centroids and $\alpha \geq 1$, one2all efficiently assigns probabilities to points so that the clustering cost of {\em each} $Q$ with cost $V(Q) \geq V(M)/\alpha$ can be estimated well from a sample of size $O(\alpha |M|\epsilon^{-2})$.
Average Distance Queries through Weighted Samples in Graphs and Metric Spaces: High Scalability with Tight Statistical Guarantees
The estimate is based on a weighted sample of $O(\epsilon^{-2})$ pairs of points, which is computed using $O(n)$ distance computations.
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